The feedback control gain to absorb the harmonic response at a desired position in continuous vibrating structures may require an infinite product of eigenvalues. Such control gain, for distributed parameter elastic structures, improves monotonically with the increase in model order of their discrete counterparts obtained by the finite difference or finite element methods. However, the estimation of control gain, using such discrete approximations is inaccurate due to dissimilar asymptotoc behavior of eigenvalues of the discrete model and associated distributed parameter system. An alternative formula uses deformation information for determining the control gain, but for non-uniform structures a closed form expression for deformation may not exist. The objective here is to show that a new mathematical model for non-uniform structure, based on piecewise constant approximation, can be successfully used for better approximation of the control gain. For simplicity, the analysis is carried out for a non-uniform vibrating rod in order to validate the above arguments.
Zero Assignment in Continuous Systems
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Singh, AN, Singh, KV, Ram, YM, & Pang, S. "Zero Assignment in Continuous Systems." Proceedings of the ASME 2003 International Mechanical Engineering Congress and Exposition. Design Engineering, Volumes 1 and 2. Washington, DC, USA. November 15–21, 2003. pp. 1065-1071. ASME. https://doi.org/10.1115/IMECE2003-43629
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